We consider a class of linear regression model with extreme distribution noise. We show by a mean of point process technique that the asymptotic distribution of the maximum is the same as the one of the max of the noise process, under specific conditions.

We propose and study a simple stochastic model for the dynamics of a limit order book, in which arrivals of market order, limit orders and order cancellations are described in terms of a Markovian queueing system. Through its analytical tractability, the model allows to obtain analytical...

We apply a hidden Markov model of the term structure to modeling the Brazilian swap rate curve. We examine the model's characteristics and its performance in describing the cross-sectional and time-series dynamics of the term structure. Two regimes are identified, a high level and a high...

We study the first-order bifurcating autoregressive process Xt=ϕX⌊t/2⌋+ϵt with Weibull innovations. Using point process technique, we estimate the model parameter ϕ and the tail index α in the Weibull distribution and obtain the joint limit distribution of estimators.

We consider the maximum process of a random walk with additive independent noise in the form of maxi=1,…,n(Si+Yi). The random walk may have dependent increments, but its sample path is assumed to converge weakly to a fractional Brownian motion. When the largest noise has the same order as the...

A new version of dynamic time warping for samples of observed event times that are modeled as time-warped intensity processes is introduced. The approach is developed within a framework where for each experimental unit or subject in a sample, a random number of event times or random locations...

We use point processes theory to describe the asymptotic distribution of all upper order statistics for observations collected at renewal times. As a corollary, we obtain limiting theorems for corresponding extremal processes.